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the affine Hilbert-Poincare series
HilbertSeries(M:RING or TAGGED("Quotient")):TAGGED("$hp.PSeries")
This function computes the affine Hilbert-Poincare series of M.
The grading must be a positive Z^1
must have a single row with positive entries), and the ordering must
be degree compatible (i.e. for a buggy behaviour of cocoa-4,
must have all 1's in the first row).
In the standard case, i.e. the weights of all
indeterminates are 1, the result is simplified so that the power
appearing in the denominator is the dimension of M + 1.
It is exacly the same as
(i) the coefficient ring must be a field.
(ii) these functions produce tagged objects: they cannot safely be
(non-)equality to other values.
For further details on affine Hilbert functions see the book:
Kreuzer, Robbiano "Computer Commutative Algebra II", Section 5.6.
Use R ::= QQ[x,y,z];
(1 + x + x^2 + x^3) / (1-x)^2